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Sagot :
The sequences of transformations that could be applied to the parent function are (e) Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units
How to determine the sequence of transformation?
The graph that completes the question is added as an attachment
From the attached graph, we have the following points
(3, 0) and (0, 6)
Calculate the equation of the line using
[tex]g(x) = \frac{y_2 - y_1}{x_2 -x_1} * (x - x_2) + y_2[/tex]
This gives
[tex]g(x) = \frac{6 - 0}{0 -3} * (x - 0) + 6[/tex]
Evaluate the quotient
g(x) = -2 * (x) + 6
Expand
g(x) = -2x + 6
This means that the equation of the line is:
g(x) = -2x + 6
So, we have:
f(x) = x as the parent function and g(x) = -2x + 6 as the transformed function.
The transformations from f(x) to g(x) are as follows:
- Reflect over the y-axis i.e. f'(x) = -f(x) = -x
- Stretch vertically by a factor of 2 i.e. f"(x) = 2f'(x) = -2x
- Shift up by 6 units i.e. g(x) = f"(x) + 6 = -2x + 6
Hence, the sequences of transformations that could be applied to the parent function are (e) Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units
Read more about transformation at:
https://brainly.com/question/13810353
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